PROBLEM A solid, uniform, frictionless cylindrical reel of mass $\backslash ($ M$=3\mathrm{.}00\backslash$mathrm$\{$~kg$\}\backslash )$ and radius $\backslash ($ R$=0\mathrm{.}400\backslash$mathrm$\{$~m$\}\backslash )$ is used to draw water from a well $($Fig$.8\mathrm{.}28$a$).$ A bucket of mass $\backslash ($ m$=2\mathrm{.}00\backslash$mathrm$\{$~kg$\}\backslash )$ is attached to a cord that is wrapped around the cylinder. $($a$)$ Find the tension $\backslash ($ T $\backslash )$ in the cord and acceleration $\backslash ($ a $\backslash )$ of the bucket. $($b$)$ If the bucket starts from rest at the top of the well and falls for $3\mathrm{.}00$ s before hitting the water, how far does it fall?